Abstract: A screw displacement pump has a chamber. Inlet and outlet are provided for the admission of gas to and discharge of gas from the chamber. Intermeshing screw members rotatably mounted within the chamber for delivering the gas from the inlet to outlet, wherein the pitch of the screw members decrease continuoulsy from the inlet end thereof to the outlet end thereof to cause compression of the gas being delivered. The continuous reduction in the pitch distance from the inlet end to the outlet end is generated by the following relationship:Pitch at the outlet end/Pitch at the inlet end<.pi..sub.i /kwhere, .pi..sub.i =pressure ratio calculated under the condition that the process is effected in a adiabatic and the work done is constant, C.sub.1 =0, and k is gas constant.